Britain's Olympic success has helped contribute to a record boost in the number of people playing sport, according to figures released by Sport England. The grassroots funding body said that the number of adults playing sport at least once a week had increased by 750,000 in the past year.

Following a Games in which successful female athletes were particularly to the fore, the funding body that invests £240m a year in grassroots sport also said that its latest figures showed the strongest growth in participation numbers had been among women. An increase of half a million in the past year had helped to cut the gap that still exists between male and female participation.

Amid intense scrutiny of whether the London 2012 Games will buck the trend of previous Olympics and deliver on Lord Coe's promise that it would inspire more people to play more sport, Sport England's Active People survey also showed sharp increases in successful Olympic sports such as cycling and sailing.

Sport England's chief executive Jennie Price said that the sports that had done best were those that had planned to capitalise on the Games. "This is a really substantial increase," she said. "It's an awful lot given the economic conditions, the weather and the fact a lot of people spent the summer watching the Olympics.

"Some of the sports performing best are the ones with the best plans. It's no accident that cycling is performing really well and sports like hockey are right up there. Once we got rid of that awful wet start to the summer, in the three months around the Games there was a bounce in participation."

Cycling, seen as one of the sports that has most successfully married elite success and growth in participation, has increased the number cycling at least once a week by 200,000 over the past year.

"With almost two million people cycling once a week following a summer of unprecedented cycling success, this is our legacy in action," British Cycling's chief executive Ian Drake said. "British Cycling has set new standards in elite sport and with these latest figures from Sport England, we can celebrate gold-medal results in grassroots participation."

The figures, which show that 15.5m people aged 16 and over are playing sport more than once a week, represent progress on last year when a continued decline led the sports minister Hugh Robertson to declare them "very disappointing".

The coalition government was forced to drop a target set by the previous Labour administration of persuading one million more people to play sport three times or more a week by 2013. Under that measure, the total has increased by 500,000 since 2008 to 7.4 million.

"One of the key legacy ambitions from London 2012 was to get more people playing sport – something that no other host city has managed to do," Robertson claimed. "These are excellent figures and show that we are making good progress."

The government announced last year that Sport England was to adjust its focus to concentrate on building links between schools and clubs in an effort to address an ongoing decline in the number of 16- to 25-year-olds playing sport and encourage it as a habit for life.

It has also warned governing bodies, who receive a total of £450m over four years through the quango's Whole Sport Plan, that it will take a "no-compromise approach" to cutting the funding of those sports that are not delivering against their targets.

The latest figures show there has been no statistically significant increase in the number of 16- to 25-year-olds playing sport since the last Active People survey results were released a year ago. "Most of the work we're doing with young people really kicks in in 2013. We have to understand that this is the hardest group to move. They play more sport than anyone else already and they've got a massive amount of choice about their free time," said Price, who has been under intense pressure to show that the public money invested in grassroots sport is having an effect.

Cycling, athletics and swimming have shown the most growth while cricket – which suffered as a result of the wet summer – and table tennis were the biggest losers. Around two thirds of sports showed an increase, but a third declined.

Later this month, sports governing bodies will find out the level of their funding awards for the next four years. The Guardian recently revealed that the government had scrapped plans to merge Sport England with the elite funding agency UK Sport. Instead, they will be asked to find ways of cutting back office costs and working more effectively together.

As a result of the spending cuts announced this week by the government, Sport England's exchequer funding – around a third of its total – will be reduced by 1% this year and around 2% next year.